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Q.

One end of a spring of force constant K is fixed to a vertical wall and the other to a body of mass m resting on a smooth horizontal surface. There is another wall at a distance x0 from the body. The spring is then compressed by 3x0 and released. The time taken to strike the wall from the instant of release is (given sin-1(l/3) = (π/9))

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a

π6mK

b

2π3mK

c

π4mK

d

11π9mK

answer is D.

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Detailed Solution

When spring is compressed by 3x0. Amplitude, A=3x0. The time taken from extreme compressed position to mean position, t1=T/4. If time taken (t2) from mean position to x=x0 is given byx=A sin2πt2T     ⇒        x0=3x0 sin 2πt2T sin 2πt2T=13      ⇒     2πt2T=π9     ⇒ t2=T18 t1+t2 =T4+T18=1118T          =1182πmK=119πmK
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